Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 563 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.₹520 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹200 (b) ₹320 (c) ₹40 (d) ₹260
2. 2.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹39 (b) ₹30 (c) ₹6 (d) ₹48
3. 3.If 8 mangoes cost ₹40, how much do 6 mangoes cost? (a) ₹35 (b) ₹38 (c) ₹30 (d) ₹240
4. 4.₹102 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹102 (c) ₹34 (d) ₹68
5. 5.If 5 pens cost ₹110, how much do 2 pens cost? (a) ₹66 (b) ₹44 (c) ₹220 (d) ₹107
6. 6.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹30 (d) ₹35
7. 7.If 6 kites cost ₹114, how much do 5 kites cost? (a) ₹113 (b) ₹570 (c) ₹95 (d) ₹114
8. 8.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹30 (b) ₹90 (c) ₹15 (d) ₹75
9. 9.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹234 (d) ₹117
10. 10.If 2 notebooks cost ₹32, how much do 8 notebooks cost? (a) ₹128 (b) ₹38 (c) ₹256 (d) ₹144
11. 11.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹64 (b) ₹80 (c) ₹16 (d) ₹40
12. 12.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹28 (d) ₹35
13. 13.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹108 (b) ₹288 (c) ₹36 (d) ₹198
14. 14.If 3 notebooks cost ₹30, how much do 9 notebooks cost? (a) ₹36 (b) ₹100 (c) ₹270 (d) ₹90
15. 15.If 9 pens cost ₹99, how much do 2 pens cost? (a) ₹22 (b) ₹92 (c) ₹198 (d) ₹33
16. 16.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹250 (b) ₹275 (c) ₹300 (d) ₹50
17. 17.If 3 notebooks cost ₹27, how much do 12 notebooks cost? (a) ₹36 (b) ₹108 (c) ₹117 (d) ₹324
18. 18.₹230 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹230 (b) ₹184 (c) ₹46 (d) ₹115
19. 19.₹140 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹56 (b) ₹28 (c) ₹84 (d) ₹70
20. 20.If 4 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹132 (b) ₹55 (c) ₹144 (d) ₹528
21. 21.₹180 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹180 (b) ₹45 (c) ₹90 (d) ₹135
22. 22.If 5 pens cost ₹105, how much do 10 pens cost? (a) ₹110 (b) ₹231 (c) ₹1050 (d) ₹210
23. 23.If 2 notebooks cost ₹8, how much do 3 notebooks cost? (a) ₹24 (b) ₹12 (c) ₹9 (d) ₹16
24. 24.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 15 days (d) 8 days
25. 25.If 3 pens cost ₹36, how much do 12 pens cost? (a) ₹45 (b) ₹156 (c) ₹432 (d) ₹144
26. 26.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 9 days (d) 15 days
27. 27.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹39 (b) ₹78 (c) ₹390 (d) ₹351
28. 28.If 6 pens cost ₹60, how much do 5 pens cost? (a) ₹59 (b) ₹300 (c) ₹60 (d) ₹50
29. 29.₹259 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹185 (b) ₹74 (c) ₹37 (d) ₹222
30. 30.If 9 mangoes cost ₹45, how much do 11 mangoes cost? (a) ₹60 (b) ₹55 (c) ₹47 (d) ₹495
31. 31.If 6 kites cost ₹18, how much do 5 kites cost? (a) ₹90 (b) ₹17 (c) ₹15 (d) ₹18
32. 32.If 9 notebooks cost ₹72, how much do 5 notebooks cost? (a) ₹68 (b) ₹40 (c) ₹360 (d) ₹48
33. 33.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 2 days (d) 3 days
34. 34.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 28 days
35. 35.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 7 days (d) 6 days
36. 36.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
37. 37.If 4 kites cost ₹76, how much do 3 kites cost? (a) ₹75 (b) ₹76 (c) ₹57 (d) ₹228
38. 38.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 13 days (d) 5 days
39. 39.If 5 pens cost ₹15, how much do 6 pens cost? (a) ₹16 (b) ₹18 (c) ₹90 (d) ₹21
40. 40.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹27 (d) ₹45

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